We prove that vanishing viscosity solutions to smooth non-degenerate systems of balance laws, having small bounded variation, in one space dimension, must be functions of special bounded variation (SBV). For more than one equation, this SBV-regularity for non-degenerate fluxes is new also in the case of systems of conservation laws outside the context of genuine nonlinearity. For general smooth strictly hyperbolic systems of balance laws, this regularity fails, as known for systems of conservation laws: in such case we generalize the SBV-like regularity of the eigenvalue functions of the Jacobian matrix of the flux from conservation to balance laws. Proofs are based on extending Oleinink-type balance estimates, with the introduction of new source measure, a localization argument from previous works, and observations in real analysis.

SBV regularity of Entropy Solutions for Hyperbolic Systems of Balance Laws with General Flux function

Ancona, Fabio;Caravenna, Laura
;
Marson, Andrea
2025

Abstract

We prove that vanishing viscosity solutions to smooth non-degenerate systems of balance laws, having small bounded variation, in one space dimension, must be functions of special bounded variation (SBV). For more than one equation, this SBV-regularity for non-degenerate fluxes is new also in the case of systems of conservation laws outside the context of genuine nonlinearity. For general smooth strictly hyperbolic systems of balance laws, this regularity fails, as known for systems of conservation laws: in such case we generalize the SBV-like regularity of the eigenvalue functions of the Jacobian matrix of the flux from conservation to balance laws. Proofs are based on extending Oleinink-type balance estimates, with the introduction of new source measure, a localization argument from previous works, and observations in real analysis.
File in questo prodotto:
File Dimensione Formato  
s00030-025-01064-4.pdf

accesso aperto

Descrizione: Ancona, F., Caravenna, L. & Marson, A. SBV regularity of Entropy Solutions for Hyperbolic Systems of Balance Laws with General Flux function. Nonlinear Differ. Equ. Appl. 32, 73 (2025). https://doi.org/10.1007/s00030-025-01064-4
Tipologia: Published (Publisher's Version of Record)
Licenza: Creative commons
Dimensione 1.05 MB
Formato Adobe PDF
1.05 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3555199
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
  • OpenAlex ND
social impact